Decision Theoretic Foundations for Conformal Prediction: Optimal Uncertainty Quantification for Risk-Averse Agents
This work addresses uncertainty quantification for risk-sensitive domains such as medicine, providing foundational decision-theoretic insights that are incremental but with strong practical implications.
The paper tackles the problem of quantifying prediction uncertainty for risk-averse decision-making, proving that prediction sets are optimal for optimizing value at risk and introducing the Risk-Averse Calibration (RAC) algorithm, which experimentally shows a substantially improved trade-off between safety and utility in applications like medical diagnosis.
A fundamental question in data-driven decision making is how to quantify the uncertainty of predictions in ways that can usefully inform downstream action. This interface between prediction uncertainty and decision-making is especially important in risk-sensitive domains, such as medicine. In this paper, we develop decision-theoretic foundations that connect uncertainty quantification using prediction sets with risk-averse decision-making. Specifically, we answer three fundamental questions: (1) What is the correct notion of uncertainty quantification for risk-averse decision makers? We prove that prediction sets are optimal for decision makers who wish to optimize their value at risk. (2) What is the optimal policy that a risk averse decision maker should use to map prediction sets to actions? We show that a simple max-min decision policy is optimal for risk-averse decision makers. Finally, (3) How can we derive prediction sets that are optimal for such decision makers? We provide an exact characterization in the population regime and a distribution free finite-sample construction. Answering these questions naturally leads to an algorithm, Risk-Averse Calibration (RAC), which follows a provably optimal design for deriving action policies from predictions. RAC is designed to be both practical-capable of leveraging the quality of predictions in a black-box manner to enhance downstream utility-and safe-adhering to a user-defined risk threshold and optimizing the corresponding risk quantile of the user's downstream utility. Finally, we experimentally demonstrate the significant advantages of RAC in applications such as medical diagnosis and recommendation systems. Specifically, we show that RAC achieves a substantially improved trade-off between safety and utility, offering higher utility compared to existing methods while maintaining the safety guarantee.